Primal Dual Affine Scaling on GPUs

TL;DR

This paper introduces a GPU-based implementation of the Primal-Dual Affine Scaling method for linear optimization, including novel techniques for system conversion, solving symmetric subsystems, and reducing memory usage.

Contribution

It presents new GPU-compatible algorithms and strategies for efficient linear optimization solving using the Primal-Dual Affine Scaling method.

Findings

Efficient GPU implementation of the method.

New CUDA techniques for symmetric system solving.

Strategies to minimize memory transfer and storage.

Abstract

Here we present an implementation of Primal-Dual Affine scaling method to solve linear optimization problem on GPU based systems. Strategies to convert the system generated by complementary slackness theorem into a symmetric system are given. A new CUDA friendly technique to solve the resulting symmetric positive definite subsystem is also developed. Various strategies to reduce the memory transfer and storage requirements were also explored.